“Right now we’ve got about 63, but we’re going to the floor with an open amendment process,” Hoeven said on "Fox News Sunday." “We’re trying to foster more bipartisanship, getting the Senate to work the way it’s supposed to work, so we can pass this measure and other measures and either override the veto or attach the bill to other legislation that will get 67 votes.”

Last week, the House approved construction of the Keystone XL pipeline in a vote of 266 to 153. The legislation now goes to the Senate, where it is expected to pass, but the White House has warned that President Obama would veto the bill. The Senate needs 67 votes to override a presidential veto.